TSTP Solution File: SEU221+1 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : SEU221+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s

% Computer : n005.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 31 18:32:37 EDT 2022

% Result   : Theorem 1.49s 0.56s
% Output   : Refutation 1.49s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   81 (  16 unt;   0 def)
%            Number of atoms       :  427 ( 128 equ)
%            Maximal formula atoms :   19 (   5 avg)
%            Number of connectives :  556 ( 210   ~; 206   |; 106   &)
%                                         (  10 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :   11 (  11 usr;   2 con; 0-2 aty)
%            Number of variables   :  108 (  91   !;  17   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f490,plain,
    $false,
    inference(subsumption_resolution,[],[f489,f237]) ).

fof(f237,plain,
    relation(sF15),
    inference(subsumption_resolution,[],[f236,f145]) ).

fof(f145,plain,
    function(sK4),
    inference(cnf_transformation,[],[f97]) ).

fof(f97,plain,
    ( relation(sK4)
    & function(sK4)
    & ~ one_to_one(function_inverse(sK4))
    & one_to_one(sK4) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f83,f96]) ).

fof(f96,plain,
    ( ? [X0] :
        ( relation(X0)
        & function(X0)
        & ~ one_to_one(function_inverse(X0))
        & one_to_one(X0) )
   => ( relation(sK4)
      & function(sK4)
      & ~ one_to_one(function_inverse(sK4))
      & one_to_one(sK4) ) ),
    introduced(choice_axiom,[]) ).

fof(f83,plain,
    ? [X0] :
      ( relation(X0)
      & function(X0)
      & ~ one_to_one(function_inverse(X0))
      & one_to_one(X0) ),
    inference(flattening,[],[f82]) ).

fof(f82,plain,
    ? [X0] :
      ( ~ one_to_one(function_inverse(X0))
      & one_to_one(X0)
      & relation(X0)
      & function(X0) ),
    inference(ennf_transformation,[],[f37]) ).

fof(f37,negated_conjecture,
    ~ ! [X0] :
        ( ( relation(X0)
          & function(X0) )
       => ( one_to_one(X0)
         => one_to_one(function_inverse(X0)) ) ),
    inference(negated_conjecture,[],[f36]) ).

fof(f36,conjecture,
    ! [X0] :
      ( ( relation(X0)
        & function(X0) )
     => ( one_to_one(X0)
       => one_to_one(function_inverse(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t62_funct_1) ).

fof(f236,plain,
    ( ~ function(sK4)
    | relation(sF15) ),
    inference(subsumption_resolution,[],[f235,f146]) ).

fof(f146,plain,
    relation(sK4),
    inference(cnf_transformation,[],[f97]) ).

fof(f235,plain,
    ( ~ relation(sK4)
    | ~ function(sK4)
    | relation(sF15) ),
    inference(superposition,[],[f171,f203]) ).

fof(f203,plain,
    function_inverse(sK4) = sF15,
    introduced(function_definition,[]) ).

fof(f171,plain,
    ! [X0] :
      ( relation(function_inverse(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0] :
      ( ~ function(X0)
      | ( relation(function_inverse(X0))
        & function(function_inverse(X0)) )
      | ~ relation(X0) ),
    inference(flattening,[],[f80]) ).

fof(f80,plain,
    ! [X0] :
      ( ( relation(function_inverse(X0))
        & function(function_inverse(X0)) )
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( relation(function_inverse(X0))
        & function(function_inverse(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).

fof(f489,plain,
    ~ relation(sF15),
    inference(subsumption_resolution,[],[f488,f204]) ).

fof(f204,plain,
    ~ one_to_one(sF15),
    inference(definition_folding,[],[f144,f203]) ).

fof(f144,plain,
    ~ one_to_one(function_inverse(sK4)),
    inference(cnf_transformation,[],[f97]) ).

fof(f488,plain,
    ( one_to_one(sF15)
    | ~ relation(sF15) ),
    inference(subsumption_resolution,[],[f487,f234]) ).

fof(f234,plain,
    function(sF15),
    inference(subsumption_resolution,[],[f233,f146]) ).

fof(f233,plain,
    ( function(sF15)
    | ~ relation(sK4) ),
    inference(subsumption_resolution,[],[f232,f145]) ).

fof(f232,plain,
    ( ~ function(sK4)
    | function(sF15)
    | ~ relation(sK4) ),
    inference(superposition,[],[f170,f203]) ).

fof(f170,plain,
    ! [X0] :
      ( function(function_inverse(X0))
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f81]) ).

fof(f487,plain,
    ( ~ function(sF15)
    | one_to_one(sF15)
    | ~ relation(sF15) ),
    inference(trivial_inequality_removal,[],[f485]) ).

fof(f485,plain,
    ( one_to_one(sF15)
    | ~ function(sF15)
    | sK2(sF15) != sK2(sF15)
    | ~ relation(sF15) ),
    inference(superposition,[],[f134,f475]) ).

fof(f475,plain,
    sK3(sF15) = sK2(sF15),
    inference(backward_demodulation,[],[f471,f474]) ).

fof(f474,plain,
    apply(sK4,apply(sF15,sK2(sF15))) = sK2(sF15),
    inference(subsumption_resolution,[],[f473,f204]) ).

fof(f473,plain,
    ( apply(sK4,apply(sF15,sK2(sF15))) = sK2(sF15)
    | one_to_one(sF15) ),
    inference(subsumption_resolution,[],[f472,f234]) ).

fof(f472,plain,
    ( ~ function(sF15)
    | one_to_one(sF15)
    | apply(sK4,apply(sF15,sK2(sF15))) = sK2(sF15) ),
    inference(subsumption_resolution,[],[f465,f237]) ).

fof(f465,plain,
    ( ~ relation(sF15)
    | ~ function(sF15)
    | one_to_one(sF15)
    | apply(sK4,apply(sF15,sK2(sF15))) = sK2(sF15) ),
    inference(resolution,[],[f393,f132]) ).

fof(f132,plain,
    ! [X0] :
      ( in(sK2(X0),relation_dom(X0))
      | one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ( ( one_to_one(X0)
          | ( sK2(X0) != sK3(X0)
            & in(sK3(X0),relation_dom(X0))
            & in(sK2(X0),relation_dom(X0))
            & apply(X0,sK2(X0)) = apply(X0,sK3(X0)) ) )
        & ( ! [X3,X4] :
              ( X3 = X4
              | ~ in(X4,relation_dom(X0))
              | ~ in(X3,relation_dom(X0))
              | apply(X0,X3) != apply(X0,X4) )
          | ~ one_to_one(X0) ) )
      | ~ function(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f91,f92]) ).

fof(f92,plain,
    ! [X0] :
      ( ? [X1,X2] :
          ( X1 != X2
          & in(X2,relation_dom(X0))
          & in(X1,relation_dom(X0))
          & apply(X0,X1) = apply(X0,X2) )
     => ( sK2(X0) != sK3(X0)
        & in(sK3(X0),relation_dom(X0))
        & in(sK2(X0),relation_dom(X0))
        & apply(X0,sK2(X0)) = apply(X0,sK3(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f91,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ( ( one_to_one(X0)
          | ? [X1,X2] :
              ( X1 != X2
              & in(X2,relation_dom(X0))
              & in(X1,relation_dom(X0))
              & apply(X0,X1) = apply(X0,X2) ) )
        & ( ! [X3,X4] :
              ( X3 = X4
              | ~ in(X4,relation_dom(X0))
              | ~ in(X3,relation_dom(X0))
              | apply(X0,X3) != apply(X0,X4) )
          | ~ one_to_one(X0) ) )
      | ~ function(X0) ),
    inference(rectify,[],[f90]) ).

fof(f90,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ( ( one_to_one(X0)
          | ? [X2,X1] :
              ( X1 != X2
              & in(X1,relation_dom(X0))
              & in(X2,relation_dom(X0))
              & apply(X0,X1) = apply(X0,X2) ) )
        & ( ! [X2,X1] :
              ( X1 = X2
              | ~ in(X1,relation_dom(X0))
              | ~ in(X2,relation_dom(X0))
              | apply(X0,X1) != apply(X0,X2) )
          | ~ one_to_one(X0) ) )
      | ~ function(X0) ),
    inference(nnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0] :
      ( ~ relation(X0)
      | ( one_to_one(X0)
      <=> ! [X2,X1] :
            ( X1 = X2
            | ~ in(X1,relation_dom(X0))
            | ~ in(X2,relation_dom(X0))
            | apply(X0,X1) != apply(X0,X2) ) )
      | ~ function(X0) ),
    inference(flattening,[],[f61]) ).

fof(f61,plain,
    ! [X0] :
      ( ( ! [X2,X1] :
            ( X1 = X2
            | apply(X0,X1) != apply(X0,X2)
            | ~ in(X2,relation_dom(X0))
            | ~ in(X1,relation_dom(X0)) )
      <=> one_to_one(X0) )
      | ~ relation(X0)
      | ~ function(X0) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0] :
      ( ( relation(X0)
        & function(X0) )
     => ( ! [X2,X1] :
            ( ( apply(X0,X1) = apply(X0,X2)
              & in(X2,relation_dom(X0))
              & in(X1,relation_dom(X0)) )
           => X1 = X2 )
      <=> one_to_one(X0) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X0] :
      ( ( relation(X0)
        & function(X0) )
     => ( one_to_one(X0)
      <=> ! [X2,X1] :
            ( ( apply(X0,X1) = apply(X0,X2)
              & in(X2,relation_dom(X0))
              & in(X1,relation_dom(X0)) )
           => X1 = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_funct_1) ).

fof(f393,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sF15))
      | apply(sK4,apply(sF15,X0)) = X0 ),
    inference(forward_demodulation,[],[f392,f203]) ).

fof(f392,plain,
    ! [X0] :
      ( apply(sK4,apply(function_inverse(sK4),X0)) = X0
      | ~ in(X0,relation_dom(sF15)) ),
    inference(subsumption_resolution,[],[f391,f143]) ).

fof(f143,plain,
    one_to_one(sK4),
    inference(cnf_transformation,[],[f97]) ).

fof(f391,plain,
    ! [X0] :
      ( ~ one_to_one(sK4)
      | ~ in(X0,relation_dom(sF15))
      | apply(sK4,apply(function_inverse(sK4),X0)) = X0 ),
    inference(subsumption_resolution,[],[f390,f146]) ).

fof(f390,plain,
    ! [X0] :
      ( ~ in(X0,relation_dom(sF15))
      | ~ relation(sK4)
      | apply(sK4,apply(function_inverse(sK4),X0)) = X0
      | ~ one_to_one(sK4) ),
    inference(subsumption_resolution,[],[f385,f145]) ).

fof(f385,plain,
    ! [X0] :
      ( ~ function(sK4)
      | ~ one_to_one(sK4)
      | apply(sK4,apply(function_inverse(sK4),X0)) = X0
      | ~ relation(sK4)
      | ~ in(X0,relation_dom(sF15)) ),
    inference(superposition,[],[f166,f383]) ).

fof(f383,plain,
    relation_rng(sK4) = relation_dom(sF15),
    inference(subsumption_resolution,[],[f382,f234]) ).

fof(f382,plain,
    ( relation_rng(sK4) = relation_dom(sF15)
    | ~ function(sF15) ),
    inference(subsumption_resolution,[],[f381,f145]) ).

fof(f381,plain,
    ( ~ function(sK4)
    | ~ function(sF15)
    | relation_rng(sK4) = relation_dom(sF15) ),
    inference(subsumption_resolution,[],[f380,f143]) ).

fof(f380,plain,
    ( ~ one_to_one(sK4)
    | ~ function(sK4)
    | ~ function(sF15)
    | relation_rng(sK4) = relation_dom(sF15) ),
    inference(subsumption_resolution,[],[f379,f237]) ).

fof(f379,plain,
    ( relation_rng(sK4) = relation_dom(sF15)
    | ~ relation(sF15)
    | ~ one_to_one(sK4)
    | ~ function(sF15)
    | ~ function(sK4) ),
    inference(subsumption_resolution,[],[f376,f146]) ).

fof(f376,plain,
    ( ~ relation(sK4)
    | ~ function(sF15)
    | relation_rng(sK4) = relation_dom(sF15)
    | ~ one_to_one(sK4)
    | ~ function(sK4)
    | ~ relation(sF15) ),
    inference(superposition,[],[f197,f203]) ).

fof(f197,plain,
    ! [X0] :
      ( ~ relation(function_inverse(X0))
      | ~ function(function_inverse(X0))
      | ~ function(X0)
      | relation_rng(X0) = relation_dom(function_inverse(X0))
      | ~ relation(X0)
      | ~ one_to_one(X0) ),
    inference(equality_resolution,[],[f159]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( ~ relation(X1)
      | ~ function(X1)
      | relation_rng(X0) = relation_dom(X1)
      | function_inverse(X0) != X1
      | ~ relation(X0)
      | ~ function(X0)
      | ~ one_to_one(X0) ),
    inference(cnf_transformation,[],[f105]) ).

fof(f105,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ relation(X1)
          | ~ function(X1)
          | ( ( ( relation_rng(X0) = relation_dom(X1)
                & ! [X2,X3] :
                    ( ( ( apply(X0,X2) = X3
                        & in(X2,relation_dom(X0)) )
                      | apply(X1,X3) != X2
                      | ~ in(X3,relation_rng(X0)) )
                    & sP0(X3,X2,X0,X1) ) )
              | function_inverse(X0) != X1 )
            & ( function_inverse(X0) = X1
              | relation_rng(X0) != relation_dom(X1)
              | ( ( apply(X0,sK5(X0,X1)) != sK6(X0,X1)
                  | ~ in(sK5(X0,X1),relation_dom(X0)) )
                & sK5(X0,X1) = apply(X1,sK6(X0,X1))
                & in(sK6(X0,X1),relation_rng(X0)) )
              | ~ sP0(sK6(X0,X1),sK5(X0,X1),X0,X1) ) ) )
      | ~ relation(X0)
      | ~ function(X0)
      | ~ one_to_one(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6])],[f103,f104]) ).

fof(f104,plain,
    ! [X0,X1] :
      ( ? [X4,X5] :
          ( ( ( apply(X0,X4) != X5
              | ~ in(X4,relation_dom(X0)) )
            & apply(X1,X5) = X4
            & in(X5,relation_rng(X0)) )
          | ~ sP0(X5,X4,X0,X1) )
     => ( ( ( apply(X0,sK5(X0,X1)) != sK6(X0,X1)
            | ~ in(sK5(X0,X1),relation_dom(X0)) )
          & sK5(X0,X1) = apply(X1,sK6(X0,X1))
          & in(sK6(X0,X1),relation_rng(X0)) )
        | ~ sP0(sK6(X0,X1),sK5(X0,X1),X0,X1) ) ),
    introduced(choice_axiom,[]) ).

fof(f103,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ relation(X1)
          | ~ function(X1)
          | ( ( ( relation_rng(X0) = relation_dom(X1)
                & ! [X2,X3] :
                    ( ( ( apply(X0,X2) = X3
                        & in(X2,relation_dom(X0)) )
                      | apply(X1,X3) != X2
                      | ~ in(X3,relation_rng(X0)) )
                    & sP0(X3,X2,X0,X1) ) )
              | function_inverse(X0) != X1 )
            & ( function_inverse(X0) = X1
              | relation_rng(X0) != relation_dom(X1)
              | ? [X4,X5] :
                  ( ( ( apply(X0,X4) != X5
                      | ~ in(X4,relation_dom(X0)) )
                    & apply(X1,X5) = X4
                    & in(X5,relation_rng(X0)) )
                  | ~ sP0(X5,X4,X0,X1) ) ) ) )
      | ~ relation(X0)
      | ~ function(X0)
      | ~ one_to_one(X0) ),
    inference(rectify,[],[f102]) ).

fof(f102,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ relation(X1)
          | ~ function(X1)
          | ( ( ( relation_rng(X0) = relation_dom(X1)
                & ! [X2,X3] :
                    ( ( ( apply(X0,X2) = X3
                        & in(X2,relation_dom(X0)) )
                      | apply(X1,X3) != X2
                      | ~ in(X3,relation_rng(X0)) )
                    & sP0(X3,X2,X0,X1) ) )
              | function_inverse(X0) != X1 )
            & ( function_inverse(X0) = X1
              | relation_rng(X0) != relation_dom(X1)
              | ? [X2,X3] :
                  ( ( ( apply(X0,X2) != X3
                      | ~ in(X2,relation_dom(X0)) )
                    & apply(X1,X3) = X2
                    & in(X3,relation_rng(X0)) )
                  | ~ sP0(X3,X2,X0,X1) ) ) ) )
      | ~ relation(X0)
      | ~ function(X0)
      | ~ one_to_one(X0) ),
    inference(flattening,[],[f101]) ).

fof(f101,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ relation(X1)
          | ~ function(X1)
          | ( ( ( relation_rng(X0) = relation_dom(X1)
                & ! [X2,X3] :
                    ( ( ( apply(X0,X2) = X3
                        & in(X2,relation_dom(X0)) )
                      | apply(X1,X3) != X2
                      | ~ in(X3,relation_rng(X0)) )
                    & sP0(X3,X2,X0,X1) ) )
              | function_inverse(X0) != X1 )
            & ( function_inverse(X0) = X1
              | relation_rng(X0) != relation_dom(X1)
              | ? [X2,X3] :
                  ( ( ( apply(X0,X2) != X3
                      | ~ in(X2,relation_dom(X0)) )
                    & apply(X1,X3) = X2
                    & in(X3,relation_rng(X0)) )
                  | ~ sP0(X3,X2,X0,X1) ) ) ) )
      | ~ relation(X0)
      | ~ function(X0)
      | ~ one_to_one(X0) ),
    inference(nnf_transformation,[],[f87]) ).

fof(f87,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ relation(X1)
          | ~ function(X1)
          | ( ( relation_rng(X0) = relation_dom(X1)
              & ! [X2,X3] :
                  ( ( ( apply(X0,X2) = X3
                      & in(X2,relation_dom(X0)) )
                    | apply(X1,X3) != X2
                    | ~ in(X3,relation_rng(X0)) )
                  & sP0(X3,X2,X0,X1) ) )
          <=> function_inverse(X0) = X1 ) )
      | ~ relation(X0)
      | ~ function(X0)
      | ~ one_to_one(X0) ),
    inference(definition_folding,[],[f59,f86]) ).

fof(f86,plain,
    ! [X3,X2,X0,X1] :
      ( sP0(X3,X2,X0,X1)
    <=> ( apply(X0,X2) != X3
        | ~ in(X2,relation_dom(X0))
        | ( in(X3,relation_rng(X0))
          & apply(X1,X3) = X2 ) ) ),
    introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).

fof(f59,plain,
    ! [X0] :
      ( ! [X1] :
          ( ~ relation(X1)
          | ~ function(X1)
          | ( ( relation_rng(X0) = relation_dom(X1)
              & ! [X2,X3] :
                  ( ( ( apply(X0,X2) = X3
                      & in(X2,relation_dom(X0)) )
                    | apply(X1,X3) != X2
                    | ~ in(X3,relation_rng(X0)) )
                  & ( apply(X0,X2) != X3
                    | ~ in(X2,relation_dom(X0))
                    | ( in(X3,relation_rng(X0))
                      & apply(X1,X3) = X2 ) ) ) )
          <=> function_inverse(X0) = X1 ) )
      | ~ relation(X0)
      | ~ function(X0)
      | ~ one_to_one(X0) ),
    inference(flattening,[],[f58]) ).

fof(f58,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( ! [X3,X2] :
                  ( ( ( in(X3,relation_rng(X0))
                      & apply(X1,X3) = X2 )
                    | apply(X0,X2) != X3
                    | ~ in(X2,relation_dom(X0)) )
                  & ( ( apply(X0,X2) = X3
                      & in(X2,relation_dom(X0)) )
                    | ~ in(X3,relation_rng(X0))
                    | apply(X1,X3) != X2 ) )
              & relation_rng(X0) = relation_dom(X1) )
          <=> function_inverse(X0) = X1 )
          | ~ function(X1)
          | ~ relation(X1) )
      | ~ one_to_one(X0)
      | ~ function(X0)
      | ~ relation(X0) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
       => ! [X1] :
            ( ( function(X1)
              & relation(X1) )
           => ( ( ! [X3,X2] :
                    ( ( ( apply(X0,X2) = X3
                        & in(X2,relation_dom(X0)) )
                     => ( in(X3,relation_rng(X0))
                        & apply(X1,X3) = X2 ) )
                    & ( ( in(X3,relation_rng(X0))
                        & apply(X1,X3) = X2 )
                     => ( apply(X0,X2) = X3
                        & in(X2,relation_dom(X0)) ) ) )
                & relation_rng(X0) = relation_dom(X1) )
            <=> function_inverse(X0) = X1 ) ) ) ),
    inference(rectify,[],[f34]) ).

fof(f34,axiom,
    ! [X0] :
      ( ( function(X0)
        & relation(X0) )
     => ( one_to_one(X0)
       => ! [X1] :
            ( ( function(X1)
              & relation(X1) )
           => ( ( relation_rng(X0) = relation_dom(X1)
                & ! [X3,X2] :
                    ( ( ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) )
                     => ( apply(X0,X3) = X2
                        & in(X3,relation_dom(X0)) ) )
                    & ( ( apply(X0,X3) = X2
                        & in(X3,relation_dom(X0)) )
                     => ( apply(X1,X2) = X3
                        & in(X2,relation_rng(X0)) ) ) ) )
            <=> function_inverse(X0) = X1 ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).

fof(f166,plain,
    ! [X0,X1] :
      ( ~ in(X0,relation_rng(X1))
      | ~ relation(X1)
      | apply(X1,apply(function_inverse(X1),X0)) = X0
      | ~ function(X1)
      | ~ one_to_one(X1) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,plain,
    ! [X0,X1] :
      ( ~ in(X0,relation_rng(X1))
      | ~ relation(X1)
      | ~ one_to_one(X1)
      | ( apply(X1,apply(function_inverse(X1),X0)) = X0
        & apply(relation_composition(function_inverse(X1),X1),X0) = X0 )
      | ~ function(X1) ),
    inference(flattening,[],[f56]) ).

fof(f56,plain,
    ! [X1,X0] :
      ( ( apply(X1,apply(function_inverse(X1),X0)) = X0
        & apply(relation_composition(function_inverse(X1),X1),X0) = X0 )
      | ~ one_to_one(X1)
      | ~ in(X0,relation_rng(X1))
      | ~ relation(X1)
      | ~ function(X1) ),
    inference(ennf_transformation,[],[f35]) ).

fof(f35,axiom,
    ! [X1,X0] :
      ( ( relation(X1)
        & function(X1) )
     => ( ( one_to_one(X1)
          & in(X0,relation_rng(X1)) )
       => ( apply(X1,apply(function_inverse(X1),X0)) = X0
          & apply(relation_composition(function_inverse(X1),X1),X0) = X0 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).

fof(f471,plain,
    sK3(sF15) = apply(sK4,apply(sF15,sK2(sF15))),
    inference(forward_demodulation,[],[f470,f356]) ).

fof(f356,plain,
    apply(sF15,sK3(sF15)) = apply(sF15,sK2(sF15)),
    inference(subsumption_resolution,[],[f355,f237]) ).

fof(f355,plain,
    ( ~ relation(sF15)
    | apply(sF15,sK3(sF15)) = apply(sF15,sK2(sF15)) ),
    inference(subsumption_resolution,[],[f354,f234]) ).

fof(f354,plain,
    ( ~ function(sF15)
    | apply(sF15,sK3(sF15)) = apply(sF15,sK2(sF15))
    | ~ relation(sF15) ),
    inference(resolution,[],[f131,f204]) ).

fof(f131,plain,
    ! [X0] :
      ( one_to_one(X0)
      | ~ relation(X0)
      | apply(X0,sK2(X0)) = apply(X0,sK3(X0))
      | ~ function(X0) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f470,plain,
    sK3(sF15) = apply(sK4,apply(sF15,sK3(sF15))),
    inference(subsumption_resolution,[],[f469,f204]) ).

fof(f469,plain,
    ( sK3(sF15) = apply(sK4,apply(sF15,sK3(sF15)))
    | one_to_one(sF15) ),
    inference(subsumption_resolution,[],[f468,f234]) ).

fof(f468,plain,
    ( ~ function(sF15)
    | one_to_one(sF15)
    | sK3(sF15) = apply(sK4,apply(sF15,sK3(sF15))) ),
    inference(subsumption_resolution,[],[f466,f237]) ).

fof(f466,plain,
    ( ~ relation(sF15)
    | one_to_one(sF15)
    | ~ function(sF15)
    | sK3(sF15) = apply(sK4,apply(sF15,sK3(sF15))) ),
    inference(resolution,[],[f393,f133]) ).

fof(f133,plain,
    ! [X0] :
      ( in(sK3(X0),relation_dom(X0))
      | ~ relation(X0)
      | ~ function(X0)
      | one_to_one(X0) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f134,plain,
    ! [X0] :
      ( sK2(X0) != sK3(X0)
      | ~ function(X0)
      | one_to_one(X0)
      | ~ relation(X0) ),
    inference(cnf_transformation,[],[f93]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : SEU221+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.34  % Computer : n005.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 14:51:48 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.19/0.50  % (27959)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50  % (27958)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.50  % (27958)Instruction limit reached!
% 0.19/0.50  % (27958)------------------------------
% 0.19/0.50  % (27958)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.50  % (27958)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.50  % (27958)Termination reason: Unknown
% 0.19/0.51  % (27958)Termination phase: Preprocessing 3
% 0.19/0.51  
% 0.19/0.51  % (27958)Memory used [KB]: 895
% 0.19/0.51  % (27958)Time elapsed: 0.002 s
% 0.19/0.51  % (27958)Instructions burned: 2 (million)
% 0.19/0.51  % (27958)------------------------------
% 0.19/0.51  % (27958)------------------------------
% 0.19/0.51  % (27962)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.51  % (27960)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.51  % (27950)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.19/0.51  % (27972)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.51  % (27955)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.51  % (27965)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.19/0.51  % (27967)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.19/0.51  % (27975)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.19/0.51  % (27951)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.19/0.52  % (27973)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.19/0.52  % (27963)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.52  % (27964)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.52  % (27957)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.52  % (27971)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 0.19/0.52  % (27951)Refutation not found, incomplete strategy% (27951)------------------------------
% 0.19/0.52  % (27951)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (27954)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.52  % (27957)Instruction limit reached!
% 0.19/0.52  % (27957)------------------------------
% 0.19/0.52  % (27957)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.52  % (27957)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (27957)Termination reason: Unknown
% 0.19/0.52  % (27957)Termination phase: Saturation
% 0.19/0.52  
% 0.19/0.52  % (27957)Memory used [KB]: 5500
% 0.19/0.52  % (27957)Time elapsed: 0.133 s
% 0.19/0.52  % (27957)Instructions burned: 7 (million)
% 0.19/0.52  % (27957)------------------------------
% 0.19/0.52  % (27957)------------------------------
% 0.19/0.52  % (27951)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.52  % (27951)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.52  % (27952)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.52  
% 0.19/0.52  % (27951)Memory used [KB]: 5500
% 0.19/0.52  % (27951)Time elapsed: 0.118 s
% 0.19/0.52  % (27951)Instructions burned: 5 (million)
% 0.19/0.52  % (27951)------------------------------
% 0.19/0.52  % (27951)------------------------------
% 0.19/0.52  TRYING [1]
% 0.19/0.52  TRYING [2]
% 0.19/0.53  TRYING [3]
% 0.19/0.53  % (27974)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.53  % (27956)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53  TRYING [1]
% 0.19/0.53  % (27953)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.53  % (27969)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.53  % (27961)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.19/0.53  % (27977)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.19/0.53  TRYING [2]
% 0.19/0.53  % (27978)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.19/0.54  % (27979)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 0.19/0.54  TRYING [3]
% 0.19/0.54  % (27976)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.49/0.54  % (27970)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.49/0.55  % (27965)First to succeed.
% 1.49/0.55  % (27968)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.49/0.55  % (27966)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.49/0.55  TRYING [1]
% 1.49/0.55  TRYING [2]
% 1.49/0.55  TRYING [3]
% 1.49/0.56  % (27965)Refutation found. Thanks to Tanya!
% 1.49/0.56  % SZS status Theorem for theBenchmark
% 1.49/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 1.49/0.56  % (27965)------------------------------
% 1.49/0.56  % (27965)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.49/0.56  % (27965)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.49/0.56  % (27965)Termination reason: Refutation
% 1.49/0.56  
% 1.49/0.56  % (27965)Memory used [KB]: 1279
% 1.49/0.56  % (27965)Time elapsed: 0.160 s
% 1.49/0.56  % (27965)Instructions burned: 15 (million)
% 1.49/0.56  % (27965)------------------------------
% 1.49/0.56  % (27965)------------------------------
% 1.49/0.56  % (27949)Success in time 0.205 s
%------------------------------------------------------------------------------